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作者：Lavancier, Frederic; Philippe, Anne
作者单位：Nantes Universite
摘要：Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (J. Contemp. Math. Anal. 34(2):1-15) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian lim...
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作者：Ghosh, Subhankar; Goldstein, Larry
作者单位：University of Southern California
摘要：Let Y be a nonnegative random variable with mean mu and finite positive variance sigma(2), and let Y-s, defined on the same space as Y, have the Y size-biased distribution, characterized by E[Yf(Y)] = mu Ef(Y-s) for all functions f for which these expectations exist. Under a variety of conditions on Y and the coupling of Y and Ys, including combinations of boundedness and monotonicity, one sided concentration of measure inequalities such as p (Y - mu / sigma >= t) <= exp (-t(2) / 2(A + Bt) for...
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作者：Bossy, Mireille; Jabir, Jean-Francois; Talay, Denis
作者单位：Universite Cote d'Azur; Universidad de Chile
摘要：This paper is motivated by a new class of SDEs-PDEs systems, the so called Lagrangian stochastic models which are commonly used in the simulation of turbulent flows. We study a position-velocity system which is nonlinear in the sense of McKean. As the dynamics of the velocity depends on the conditional expectation with respect to its position, the interaction kernel is singular. We prove existence and uniqueness of the solution to the system by solving a nonlinear martingale problem and showin...
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作者：Mueller, Carl; Tribe, Roger
作者单位：University of Rochester; University of Warwick
摘要：In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is established to describe the large time evolution, distinguishing between certain death or possible life of the population.
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作者：Teixeira, Augusto
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this paper, we establish some properties of percolation for the vacant set of random interlacements, for d a parts per thousand yen 5 and small intensity u. The model of random interlacements was first introduced by Sznitman in (Ann Math, arXiv:0704.2560, 2010). It is known that, for small u, almost surely there is a unique infinite connected component in the vacant set left by the random interlacements at level u, see Sidoravicius and Sznitman (Commun Pure Appl Math 62(6):831-858, 2009) an...
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作者：Mytnik, Leonid; Perkins, Edwin
作者单位：University of British Columbia; Technion Israel Institute of Technology
摘要：We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Holder continuous of index gamma > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.
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作者：Merlevede, Florence; Peligrad, Magda; Rio, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.
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作者：Pfaffelhuber, P.; Wakolbinger, A.; Weisshaupt, H.
作者单位：University of Freiburg; Goethe University Frankfurt; University of Freiburg
摘要：A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with cA dlA g paths, infinite infinitesimal varian...
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作者：Barlow, Martin T.; Cerny, Jiri
作者单位：University of British Columbia; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process-that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud's trap model.
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作者：Morris, Robert
作者单位：University of Cambridge
摘要：We study zero-temperature Glauber dynamics on Z(d), which is a dynamic version of the Ising model of ferromagnetism. Spins are initially chosen according to a Bernoulli distribution with density p, and then the states are continuously (and randomly) updated according to the majority rule. This corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field, to one at zero temperature with no external field. Define p(c) (Z(d)) to be the infimum over p su...
